I have a dye-based Epson printer that I mainly use for printing discs, but the occasional glossy print on Epson Ultra Premium Glossy. The results look fantastic all things considering. I'm tempted to try a matte type paper, but wonder if the results are worthwhile? Everything I read suggests that pigment printers would do a lot better on matte papers.
Why not try a premium photo paper like the Epson Exhibition Fiber, Hahnemuhle Fine Art Baryta, or Harman Glossy FB AI? They are really replacing the matte papers on pigment printers in a lot of cases.
Epson Doubleweight matte works well with dye inks, as does Epson Velvet FA. Those are the two I have experience with. Did several Epson Velvet FA prints with my older dye printer have one on our picture shelf that looks good at 7 years, not 50 years but not 6 months either. You have to test any paper you are thinking of using with dye inks if they are not listed from the manufacturer or preferable on a site like Wilhelm's. Swellable Polymer coatings are best with dye inks but some of the matte and FA coatings work well too, just not to the extremes of the swellable coatings. Test under full sun or bright lights.
I am using Photo Rag Bright White (Hahnemuhle) 310 with the epson 1400/claria inks. Very pleased with the results. I haven't tried the new Epson exhibition paper. And I am holding off on the Moab and numerous other papers until I calibrate the printer via colorometer. But these are great!